This may be a controversial point of view, but unless you have a genuine reason to reach out to someone I wouldn't bother. It can be different in very small markets or for niche companies, but the larger consultancies have established recruiting processes which aren't improved by emails coming in at random times.

When I worked for one of the large firms I occasionally thought the "nice to meet you at x event, it's interesting that you did y" came across as cute, but more often the emails were unwelcome.